I get the idea of posting articles related to your site/business as a form of marketing, but how does it affect the site where the articles are posted? Do they do it for back links? Or just for the content? Besides those two things, what else might be beneficial? On that note, let me ask this, I'm considering adding an articles section or even a wiki to my Axelis website. What kind of benefit could I expect from a marketing perspective?
Sure, beneficial for both sites. What else? - depends on what you offer, I mean what service your site's about.
Benifit to site hosting article? - A lot of it depends on the quality of the articles. Most sites just host articles to build quantity (i.e. "we have 12 million articles"). While some handpick only quality articles and these usually build a loyal following of readers.
Even with crappy articles they would stand a chance of picking up some key word phrases off the SE's but if they do carry quality reprintable instead of crap they will have a lot more return visitors.
A lot of the article "hubs" put up re-hashed content for the Adsense clicks. If there site is more powerful (PR), then they have the ability to over-throw the original writer of the article, assuming the article is on their site, and gain higher rankings in the SERPS. Check your backlinks from the sites you find your article on and see how many Adsense blocks are there.